Research map / Learning theory and algorithms / Matrix and tensor methods
Unique sparse decomposition of low rank matrices
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| decrease rank r | l4-type sphere-constrained recovery · synthetic Y=AX, p=100, n=5000 | probability of recovering one column | Helped |
| decrease sparsity parameter theta (while theta >= 0.1) | l4-type sphere-constrained recovery · synthetic Y=AX, p=100, n=5000 | probability of recovering one column | Helped |
| push theta toward 0 | l4-type sphere-constrained recovery · synthetic Y=AX, p=100, n=5000 | probability of recovering one column | Hurt |
| increase sample size n | l4-type sphere-constrained recovery · synthetic Y=AX, p=100, theta=0.1 | probability of recovering one column | Helped |
| decrease theta (theta >= 0.1) or r | general power method on full-column-rank A · synthetic, n=12000, p=100 | normalized Frobenius estimation error of A | Helped |
| theta below 0.1 | general power method on full-column-rank A · synthetic, n=12000, p=100 | normalized Frobenius estimation error of A | Hurt |
| use LARS sparse PCA instead of proposed method | proposed method vs SPCA baselines · synthetic orthonormal A | estimation error of A | Hurt |
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